"... like they have some sort of emotional attachment to the garbage." They do. That's why they're hoarders. Everything they own represents a piece of their id

"... like they have some sort of emotional attachment to the garbage." They do. That's why they're hoarders. Everything they own represents a piece of their identity- their past (childhood memories, toys, etc), their present (current hobbies and interests), their future (belief that objects will be useful someday). Removing these objects is an attack on the person's identity- and calling it trash is calling their identity, hopes, and dreams trash. Severe hoarding is a serious mental illness.